Proceedings World Geothermal Congress 2015 Melbourne, Australia, 19-25 April 2015 1 Nonlinear Parameter Estimation Based on History Matching of Temperature Measurements for Single-Phase Liquid-Water Geothermal Reservoirs Mustafa Onur and Yildiray Palabiyik Department of Petroleum and Natural Gas Engineering, Istanbul Technical University, Maslak, Istanbul, Turkey onur@itu.edu.tr, palabiyik@itu.edu.tr Keywords: History Matching, Temperature Data, Analytical Solution, Single-Phase Liquid-Water Geothermal Reservoirs ABSTRACT In this study, the main objective is to investigate the use of temperature data through history matching for estimating the reservoir parameters related to fluid and heat flow. The investigation is conducted by using an analytical solution based on the modification of the analytical solution of Chekalyuk (1965) as a forward model to compute both transient pressure and temperature behaviors of a single-phase, liquid-water infinite-acting geothermal system. Our modification involves the incorporation of the skin factor into the original solution of Chekalyuk (1965) who did not consider the skin effects in temperature solution. Only, the constant-rate production tests were considered. Both the gradient based Levenberg-Marquardt and non-gradient Ensemble Kalman Filters (EnKF) have been considered as the non-linear parameter estimation methods. To simulate real cases, temperature data generated from the analytical solution were corrupted with normally distributed noise. The results show which of the reservoir parameters (e.g., skin, porosity, permeability, fluid and rock densities and heat capacities) can be reliably estimated from the sandface temperature transient data in the presence of noise, recorded during constant-rate drawdown tests. A comparison of the Levenberg- Marquardt and the EnKF in terms of estimation procedure and computational performance for the problem of interest is also provided. 1. INTRODUCTION The reservoir characterization through integration of dynamic data such as pressure, rate, etc., through history matching has become commonplace throughout the petroleum and geothermal industries. Although temperature data are routinely recorded in well test applications, the use of temperature data in addition to pressure for estimating the parameters controlling the fluid and heat flow for the purpose of reservoir characterization has been ignored in the past. The temperature data for history matching has recently attracted the attention of various researchers. In the petroleum and geothermal literature, it has been shown that temperature in addition to pressure can be a good source of data for reservoir characterization by the use of simple both lumped-parameter and distributed-parameter (1D, 2D and 3D) flow models (Onur et al. 2008a, b; Sui et al. 2008a, b; Ramazanov et al. 2010; Duru and Horne 2010a, b). To the best of the authors’ knowledge, Onur et al. (2008a) were to first to investigate the use of temperature data together with pressure data in history matching for estimating reservoir parameters of fluid and heat flow or geothermal related flow problems. Their investigation was based on a non-isothermal lumped-parameter model capable of estimating both pressure and temperature responses of a single-phase liquid-dominated geothermal reservoir idealized as a single-closed or recharged tank. Their model is solely based on the convection and neglected the conduction. Then, using this lumped-parameter model as a forward model in a gradient based history-matching algorithm [the Levenberg-Marquardt method with the restricted step procedure as described by Fletcher (1972)], they showed that one could estimate reservoir parameters such as the bulk volume and porosity of reservoir confidently if the average reservoir temperature data along with average pressure data is used for the purpose of history-matching. In another work based on the same non-isothermal lumped-parameter model, Onur et al. (2008b) also showed that if the specific heat capacity and density of the reservoir rock, recharge coefficient, recharge source temperature are added to the unknown parameter set, then the parameter estimation problem based on history matching problem becomes ill-conditioned, but one could estimate the porosity and the bulk volume of the reservoir in confidence by history matching temperature and pressure data. Later, Tureyen et al. (2009) extended the non-isothermal lumped-parameter model of Onur et al. (2008b) to a more general non- isothermal model of multiple tanks and investigated the use of temperature data in history matching for estimation of reservoir parameters from such a non-isothermal forward model. The main conclusion of Tureyen et al. (2009) is that while pressure allows estimation for only the initial pressure, pore volume, and the recharge index, the additional temperature information allows estimation for other parameters, particularly for the bulk volumes and porosities of the reservoir and aquifers. Although both the Onur et al. (2008a) and Tureyen et al. (2009) models provide useful insights on understanding of information content of average reservoir temperature in terms of model parameter estimation; nonetheless, spatial changes in pressure and temperature cannot be modeled using such lumped-parameter models, and hence cannot be used to investigate the information content of the bottom-hole pressure and temperature at a well for parameter estimation purposes. In petroleum engineering literature, a 2D (r-z) radial simulator modeling temperature response for the case of single-phase slightly compressible fluid flow in 2D stratified systems has been presented by Sui et al. (2008a). Sui et al. (2008a) have indicated that the wellbore temperature is sensitive to the radius and permeability of damage zone around the wellbore in stratified systems. In their work, although the developed energy balance equation contains the effects of Joule-Thomson and thermal expansion, pressure used in energy balance equation has been obtained from the mass balance equation that makes the assumptions of isothermal flow and slightly compressible fluid. This is the same assumption as the one used in Ramazanov et al. (2010) and Duru and Horne (2010a)’s studies. An algorithm for an inverse solution formulated as a non-linear least-squares regression problem to estimate permeability (region outside damage zone), porosity, radius and permeability of damage zone by history matching observed temperature and pressure data has been given by Sui et al. (2008b) as another study. The claim that the mentioned parameters could reliably be